If in a $\triangle ABC$,$r_1=2$,$r_2=3$ and $r_3=6$,then $a$ equals to

In order to double the frequency of the fundamental note emitted by a stretched string,the length is reduced to $\frac{3}{4}$ of the original length and the tension is changed. The factor by which the tension is to be changed is

In the figure,two parallel infinitely long current-carrying wires are shown. If the resultant magnetic field at point $A$ is zero,then determine the current $I$ (in $A$).

The r.m.s. velocity of $CO_2$ at a temperature $T$ (in kelvin) is $x \ cm \ s^{-1}$. At what temperature (in kelvin),the r.m.s. velocity of nitrous oxide would be $4 x \ cm \ s^{-1}$ (in $T$)? (Atomic weights of $C, N$ and $O$ are respectively $12, 14$ and $16$)

The solution of the differential equation $\frac{dy}{dx} - 2y \tan 2x = e^x \sec 2x$ is

If you suspect a major deficiency of antibodies in a person,to which of the following would you look for confirmatory evidence?